Question: Kevin is 18 years older than William. Five years ago, Kevin was 3 times as old as William. How old is William now?
Solution: We can use the given information to write down two equations that describe the ages of Kevin and William. Let Kevin's current age be $k$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $k = w + 18$ Five years ago, Kevin was $k - 5$ years old, and William was $w - 5$ years old. The information in the second sentence can be expressed in the following equation: $k - 5 = 3(w - 5)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to use our first equation for $k$ and substitute it into our second equation. Our first equation is: $k = w + 18$ . Substituting this into our second equation, we get the equation: $(w + 18)$ $-$ $5 = 3(w - 5)$ which combines the information about $w$ from both of our original equations. Simplifying both sides of this equation, we get: $w + 13 = 3 w - 15$ Solving for $w$ , we get: $2 w = 28$ $w = 14$.